Digital Subscriber Line (DSL) is a modem technology that enables broadband digital data to be transmitted over twisted-pair wire. DSL modems allow users to access digital networks at speeds tens to hundreds of times faster than current analog modems and basic ISDN service. A range of DSL standards has been defined, known generically as “xDSL,” wherein the various standards have different data rates and other associated features but share common principles of operation. VDSL (Very High Rate Digital Subscriber Line) is the next-generation technology in the DSL family, offering data rates up to 52 Mbit/s over short runs.
DSL modems transmit data that has been modulated in accordance with either a single-carrier or a multi-carrier modulation scheme. Single-carrier schemes for VDSL include Quadrature Amplitude Modulation (QAM) and Carrierless Amplitude Modulation (CAP). These schemes are described, for example, by Gitlin et al., in Data Communications Principles (Plenum Press, New York, 1992), pp. 334–347, which is incorporated herein by reference. In QAM, input data values are mapped for transmission to a sequence of symbols, each having a certain amplitude and phase. Each symbol can be represented by a complex number, which is a point in a two-dimensional “constellation” of symbols. Data for VDSL transmission may be coded before modulation, using any of a variety of suitable coding schemes known in the art, or may alternatively be uncoded.
DSL transmission channels are often subject to severe inter-symbol interference (ISI), due to amplitude distortion in the frequency domain. The accepted solution to this problem is to use at the receiver a feed forward equalizer (FFE) together with a decision feedback equalizer (DFE), in order to cancel interference from past signals. One of the problems caused by such a DFE is error propagation since once an error has been introduced into one of the samples, the DFE will “remember” the error over many subsequent samples.
If the channel impulse response is known, a suitable Tomlinson-Harashima precoder can be used in the transmitter, and can eliminate the need for the DFE in the receiver. Precoders of this sort are described by Wei, in an article entitled, “Generalized Square and Hexagonal Constellations for Intersymbol-Interference Channels with Generalized Tomlinson-Harashima Precoders,” published in IEEE Transactions on Communications, 42:9 (September, 1994), pp. 2713–2721, which is incorporated herein by reference. The precoder in this context is intended to compensate for inter-symbol interference caused by a channel having an equivalent discrete-time response expressed as
  1  +            ∑              i        =        1            k        ⁢                  ⁢                  h        i            ⁢                        Z                      -            i                          .            
The Tomlinson-Harashima precoder comprises a two-dimensional modulo device with a negative feedback loop. The modulo device takes each complex input symbol that it receives, r, into an output symbol s given by:si=ri−ki·2L  (1)wherein i=1,2, giving the real and imaginary parts of s and r; 2L is the modulo value; and ki is an integer such that −L≦si<L. In the feedback loop, the symbols output by the modulo device are filtered by a digital filter having a discrete time response based on the equivalent discrete-time response of the channel, without the zero-order time-domain component. In other words, the filter response in the feedback loop is given by
      ∑          i      =      1        k    ⁢          ⁢            h      i        ⁢                  Z                  -          i                    .      The filtered feedback symbols are subtracted from the modulated symbols (whether coded or uncoded) that are input to the precoder for transmission.
In the receiver, the channel-distorted symbols are input to a modulo device, which is identical to that in the precoder. Assuming that the equalizer's response is well-matched to the actual response of the channel, the symbols output by the modulo device in the receiver will be identical, to within the white Gaussian noise added by the channel, to the modulated symbols that were input to the precoder for transmission. The output symbols can then be processed by a decision device or Viterbi decoder, as appropriate, to recover the input data.
U.S. Pat. No. 5,249,200, to Chen et al., whose disclosure is incorporated herein by reference, describes a device and method for combining precoding with symbol-rate spectral shaping. A data transmitter, which transmits signals to a receiver over a transmission channel, includes a Tomlinson precoding unit and a spectral shaping unit. The equivalent channel response is determined and conveyed to the precoding and shaping units, which adjust the spectral properties of the transmitted signals in accordance with the determined channel response. The precoding and shaping units may also be used independently of one another.
A further difficulty in transmitting data over twisted pair cable at DSL rates is that a substantial amount of radio-frequency (RF) radiation is inevitably emitted. It has been found that this emission can cause serious interference with amateur radio transmissions, particularly in the HF range. For this reason, emerging technical specifications for VDSL place strict upper limits on the radiation levels that VDSL systems are allowed to generate in HF bands that are set aside for amateur radio, such as 1.81–2.0 MHz, 3.5–4.0 MHz and other, higher-frequency bands. To meet these requirements, system designers typically add notch filters in the output circuits of their modems to attenuate signals in the forbidden frequency ranges. Such notch filters complicate the design not only of VDSL transmitters, but also of receivers. The VDSL receiver must compensate not only for distortion by the communication channel, but also for the distortion introduced in the transmitter output itself by the notch filters.
The conventional solution to this problem is to use an adaptive equalizer in the receiver, comprising a Decision Feedback Equalizer (DFE) and a Forward Filter Equalizer (FFE). As a rule, both the DFE and FFE comprise finite impulse response (FIR) filters, which typically must have a relatively large number of taps with large coefficients when the notch filters are active. Decision feedback equalization is described, for example, in the above-mentioned book by Gitlin et al., pp. 500–513. The long DFE, with many large coefficients, is undesirable for a number of reasons, including:                Uncertain convergence—conventional equalization schemes may converge very slowly or may not converge at all.        Error propagation—the longer the DFE, the longer will be the error bursts due to error propagation. This problem is exacerbated by the presence of a notch filter, which tends to increase the magnitude of the DFE coefficients.        The equalizer might not converge to its optimal values, resulting in a performance loss, typically on the order of 1 dB. Advanced adaptation methods may decrease this performance loss, but at the cost of significant additional complexity.        
An alternative solution is proposed by Laamanen in PCT publication WO 98/48545, whose disclosure is incorporated herein by reference. Laamanen describes a digital transmitter and receiver connected by a channel with a channel response, wherein the transmitter includes a Tomlinson-Harashima precoder. The precoder can be used to compensate for the fixed filter sections of the transmitter and/or of the receiver, as well as for a portion of the distortion caused by the channel response. In the preferred implementation of the precoder described in this publication, the feedback filter has the form of a cascade of smaller feedback blocks, each compensating for a different part of the fixed filter sections or channel response. The receiver includes the FFE part of the equalizer (in the form of a finite impulse response [FIR] filter), but the DFE portion of the equalizer is transferred to the transmitter to form part of the feedback filter chain of the precoder. The receiver then contains only the FFE portion of the equalizer.